Czechoslovak Mathematical Journal

, Volume 55, Issue 3, pp 691–697 | Cite as

Lacunary Strong (A σ , p)-Convergence

  • Tunay Bilgin


The definition of lacunary strongly convergence is extended to the definition of lacunary strong (A σ , p)-convergence with respect to invariant mean when A is an infinite matrix and p = (p i ) is a strictly positive sequence. We study some properties and inclusion relations.


lacunary sequence invariant convergence infinite matrix 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Banach: Theorie des operation lineaires. Warszava, 1932.Google Scholar
  2. [2]
    T. Bilgin: Strong A σ-summability defined by a modulus. J. Ist. Univ. Sci. 53 (1996), 89–95.Google Scholar
  3. [3]
    T. Bilgin: Lacunary strong A-convergence with respect to a modulus. Studia Univ. Babes-Bolyai Math. 46 (2001), 39–46.Google Scholar
  4. [4]
    G. Das and S. K. Mishra: Sublinear functional and a class of conservative matrices. J. Orissa Math. 20 (1989), 64–67.Google Scholar
  5. [5]
    G. Das and B. K. Patel: Lacunary distribution of sequences. Indian J. Pure Appl. Math. 20 (1989), 64–74.Google Scholar
  6. [6]
    A. R Freedman, J. J. Sember and M. Raphed: Some Cesaro-type summability spaces. Proc. London Math. Soc. 37 (1978), 508–520.Google Scholar
  7. [7]
    G. G. Lorentz: A contribution to the theory of divergent sequences. Acta Math. 80 (1980), 167–190.Google Scholar
  8. [8]
    Mursaleen: Matrix transformations between some new sequence spaces. Houston J. Math. 4 (1983), 505–509.Google Scholar
  9. [9]
    E. Ozturk and T. Bilgin: Strongly summable sequence spaces defined by a modulus. Indian J. Pure Appl. Math. 25 (1994), 621–625.Google Scholar
  10. [10]
    S. Pehlivan and B. Fisher: Lacunary strong convergence with respect to a sequence of modulus functions. Comment. Math. Univ. Carolin. 36 (1995), 69–76.Google Scholar
  11. [11]
    E. Savas: Lacunary strong σ-convergence. Indian J. Pure Appl. Math. 21 (1990), 359–365.Google Scholar
  12. [12]
    P. Scheafer: Infinite matrices and invariant meant. Proc. Amer. Math. Soc. 36 (1972), 104–110.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • Tunay Bilgin
    • 1
  1. 1.Department of MathematicsUniversity of 100Yil VanTurkey

Personalised recommendations